A generalization of Birchs theorem and vertex-balanced steady states for generalized mass-action systems.

@article{Craciun2019AGO,
  title={A generalization of Birchs theorem and vertex-balanced steady states for generalized mass-action systems.},
  author={Gheorghe Craciun and Stefan Muller and Casian Pantea and Polly Y. Yu},
  journal={Mathematical biosciences and engineering : MBE},
  year={2019},
  volume={16 6},
  pages={
          8243-8267
        }
}
Mass-action kinetics and its generalizations appear in mathematical models of (bio)chemical reaction networks, population dynamics, and epidemiology. The dynamical systems arising from directed graphs are generally non-linear and difficult to analyze. One approach to studying them is to find conditions on the network which either imply or preclude certain dynamical properties. For example, a vertex-balanced steady state for a generalized mass-action system is a state where the net flux through… 

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